Complete multipartite graphs are determined by their distance spectra
Ya-Lei Jin, Xiao-Dong Zhang
TL;DR
This paper proves that complete multipartite graphs are uniquely identified by their distance spectra, confirming a conjecture and contrasting with their adjacency spectra which do not distinguish them.
Contribution
The paper establishes that complete multipartite graphs are determined by their distance spectra, providing a new spectral characterization.
Findings
Complete multipartite graphs are determined by their distance spectra.
Confirmed the conjecture by Lin, Hong, Wang, and Shu.
Contrasts with adjacency spectra, which do not determine these graphs.
Abstract
It is well known that the complete multipartite graphs can not be determined by their adjacency spectra. But in this paper, we prove that they can be determined by their distance spectra, which confirms the conjecture proposed by Lin, Hong, Wang and Shu.
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Taxonomy
TopicsGraph theory and applications · Graph Labeling and Dimension Problems · Finite Group Theory Research